Question

Problem 7 Suppose that in the perfectly competitive baseball cap industry, each firm has the same...

Problem 7 Suppose that in the perfectly competitive baseball cap industry, each firm has the same cost structure such that long-run average cost is minimized at 210 caps per day. The firms’ minimum long-run average cost is \$1.50. Total market demand is QD = 4000 − 100P .

(i) (2 points) What is the long-run equilibrium market price and quantity in this market?

(ii) (2 points) How many firms are in this market?

(i)

For a perfect comeptitive firm in the long run we have P = MC (Profit maximizing condition) and P = ATC(In the long run each firm earns 0 profit because when they earn positive profit new firm enters which shifts supply curve to the right and which results in decrease in price till P = ATC).

Thus we have P = MC = ATC

As MC cuts ATC at its minimum => thus here we have P = MC = min(ATC) = 1.50

Also it is given that Q = 210 when P = MC = min{ATC)

Thus each firm will produce 210 units

Hence, we have market price = 1.5 => 4000 - 1.5*100 = 3850

Hence, Market price = 1.5 and Market quantity = 3850

(ii)

Let there be N firms and each producing 210 units.

Thus, 210*N = 3850 => N = 18.33

Hence there are 18.33 firms (or 18 firms approx)